The dimension of the kernel in an intersection of starshaped sets

We establish the following Helly-type theorem: Let ${\cal K}$ be a family of compact sets in $\mathbb{R}^d$. If every d + 1 (not necessarily distinct) members of ${\cal K}$ intersect in a starshaped set whose kernel contains a translate of set A, then $\cap \{ K : K\; \hbox{in}\; {\cal K} \}$ also is a starshaped set whose kernel contains a translate of A. An analogous result holds when ${\cal K}$ is a finite family of closed sets in $\mathbb{R}^d$. Moreover, we have the following planar result: Define function f on $\{0, 1, 2\}$ by f(0) = f(2) = 3, f(1) = 4. Let ${\cal K}$ be a finite family of closed sets in the plane. For k = 0, 1, 2, if every f(k) (not necessarily distinct) members of ${\cal K}$ intersect in a starshaped set whose kernel has dimension at least k, then $\cap \{K : K\; \hbox{in}\; {\cal K}\}$ also is a starshaped set whose kernel has dimension at least k. The number f(k) is best in each case.Received: 4 June 2002     

A Simplicial elimination scheme for ⋀-semidistributive lattices and interval collapsing

The purpose of this paper is first to show that -semidistributive lattices can be characterized by a simplicial elimination scheme in the same sense as upper locally distributive lattices or antimatroids. Secondly, we show that this elimination scheme leads to an interval collapsing algorithm and a constructing algorithm for semidistributive lattices.     

Semigroup varieties with a small number of term operations

We give an equational characterization of (varieties of) semigroups having a p_n-sequence bounded above by a polynomial function of n. This is achieved by studying the syntactical connections between certain semigroup identities and their equational consequences.     

Decomposability of free Tarski algebras

In this paper we study the direct decomposability of free Tarski algebras. We show that infinite freely generated Tarski algebras are directly indecomposable, whereas finite freely generated Tarski algebras can only be decomposed into a direct product of two factors, one of which is the two-element Tarski algebra.     

A non-trivial Fréchet quotient of the space of real analytic functions

We prove that the space of real analytic functions ${\cal A}(\Omega)$ on an arbitrary open set $\Omega \subseteq \mathbb{R}^d$ has a Fréchet infinite dimensional quotient space with a continuous norm. Received: 4 February 2002     

Bounded point evaluations and cyclic polynomials on the spaces $$\hat F$$

LetF be aBK space withAK and denote the set of all formal power series with such that ε F for the sequence of coefficients of . We give a necessary and sufficient condition for a point to be a bounded point evaluation on , and for a polynomial to be cyclic in . As special cases, we obtain the results for the space ℓ _p (β) in [7]. Research of the authors supported under the research project #1232 of the Serbian Ministry of Sciences and Tecnology and, in the case of the second author, also by the DAAD foundation (German Academic Exchange Service), grant 911 103 102 8.     

Design and Power Optimization of High-Speed Pipeline ADC for Wideband CDMA Applications

This paper presents a 7-bit 64 MS/s pipeline A/D convertersuitable for wideband CDMA applications. Targeting atachieving low power dissipation at high speed, techniques suchas digital correction and optimal scaling of capacitor valuehave been employed. Switched-Opamp technique is used tofurther reduce power consumption. This ADC is implemented in0.5 m standard CMOS process. It operates from a single 3 V supply, and dissipates only 31 mW at 64 MS/s.     

A Conversation with Lee Alvin DuBridge - Part II

Physicist Lee A. DuBridge became president of the California Institute of Technology in 1946. In this interview he recalls his dealings at Caltech with Linus Pauling; his memories of George W. Beadle, Theodore von Kármán, and J. Robert Oppenheimer; the military Vista Project at Caltech; and the difficulties surrounding the deportation of Hsue-Shen Tsien, Caltech's Goddard Professor of Jet Propulsion.     

The strength of octupole correlations in neutron-rich Xe isotopes

Excited levels in ¹⁴⁰Xe and ¹⁴²Xe nuclei, populated in the spontaneous fission of ²⁴⁸Cm, were studied by means of prompt γ-ray spectroscopy, using EUROGAM2 array. We report the first observation of an octupole band in ¹⁴²Xe and extend the octupole band in ¹⁴⁰Xe. Level schemes of ¹⁴⁰Xe and ¹⁴²Xe obtained in this work show patterns characteristic of ocupole-vibrational bands. Properties of octupole bands in Xe isotopes indicate that octupole correlations in these nuclei are lower than in the corresponding Ba nuclei. The electric dipole moment of ¹⁴²Xe was found to be larger than in other Xe isotopes, contrary to theoretical predictions. This may be due to the special role of the N = 88 neutron number. Received: 18 November 2002 / Accepted: 15 December 2002 / Published online: 25 February 2003 RID="a" ID="a"e-mail: urban@fuw.edu.pl Communicated by D. Schwalm